Universal critical quantum properties of cuprate superconductors

Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature. Experimentally, these phase transitions are driven by doping and correspond to critical endpoints of the phase transition line in the temperature-hole concentration plane. Provided that the order parameter is a complex scalar in two dimensions. and that the London relation between superfluid number density and magnetic penetration depth herds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition. In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value. These predictions agree remarkably well with available experimental date and provide useful constraints for a microscopic theory.